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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 247962o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 247962.o4 | 247962o1 | \([1, 0, 1, 1583, -542044]\) | \(18191447/5271552\) | \(-127242450137088\) | \([2]\) | \(983040\) | \(1.3856\) | \(\Gamma_0(N)\)-optimal |
| 247962.o3 | 247962o2 | \([1, 0, 1, -90897, -10270940]\) | \(3440899317673/106007616\) | \(2558766145725504\) | \([2, 2]\) | \(1966080\) | \(1.7322\) | |
| 247962.o2 | 247962o3 | \([1, 0, 1, -218057, 24774356]\) | \(47504791830313/16490207448\) | \(398033520100413912\) | \([2]\) | \(3932160\) | \(2.0787\) | |
| 247962.o1 | 247962o4 | \([1, 0, 1, -1443417, -667595660]\) | \(13778603383488553/13703976\) | \(330780666274344\) | \([2]\) | \(3932160\) | \(2.0787\) |
Rank
sage: E.rank()
The elliptic curves in class 247962o have rank \(0\).
Complex multiplication
The elliptic curves in class 247962o do not have complex multiplication.Modular form 247962.2.a.o
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
